Hedge Fund Crowding and Game Theory

A couple weeks ago I came across an interesting article that I didn’t have the chance to read at the time. But I did have a spare moment this past weekend, and the topic was very timely — namely the phenomenon of hedge fund crowding and how game theory influences hedge funds’ decision on whether to hold or sell.

Game Theory and the “Prisoner’s Dilemma”

If you’re not familiar about game theory and the specific case of the “Prisoner’s Dilemma”, here’s a brief (non-mathematical) recap:

Imagine two rational, intelligent beings who are caught for a crime. The prosecutors do not have enough evidence to convict either of them, so they devise a scheme for getting them to confess. In the article, if both prisoners betray each other, they both get two years in prison. If either one betrays the other, the silent prisoner gets three years, but the betrayer gets off scot free. If both prisoners remain silent, they both get one year.

Naturally, both prisoners try to predict the other’s actions. It’s in each one’s individual interest to betray the other if they don’t consider the other’s actions. If they could communicate with each other, they would both obviously stay silent, in turn only receiving a one year sentence. So the best possible outcome (a one year sentence) is not the one most likely, as they are both afraid the other will betray him and get off scot free. It’s this human temptation that makes game theory so interesting. Acting rationally, humans don’t choose the most optimal outcome.

Hedge Fund Crowding and Game Theory

Now consider two large hedge funds that are in a shaky stock. Both funds realise that the stock will likely drop 20% in the immediate future . The hedge funds in this scenario (obviously simplified for the sake of demonstration) would cause the stock to hit a downward spiral if either of them sold. Lets say the stock would drop an additional 10% upon either hedge fund selling. What should each fund do?

If both funds sell, the stock would drop 20% before the first fund sells and an additional 10% before the second fund sells, so the second fund would take a 30% loss (20% initial + 10% from first fund sell). If one fund sells and the other holds, its the same case — one fund would take a 20% loss and the other a 30% loss. Now, if both funds hold, they would “only” take a 20% loss each. It’s in both their best interests to hold. But if they both feel the stock has nowhere to go but down, then why not sell first and ask questions later?

In this scenario, both hedge funds can communicate with each other and time their trades. They can both agree to sell or hold. But like in the first example, the human temptation to betray the other and execute the “safe” strategy of liquidating the position is the one most likely. The human emotions of fear and greed are simply too overwhelming to calmly execute a rational decision.